DLMF:19.29.E21 (Q6649)

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DLMF:19.29.E21
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    Statements

    test
    ∫ y x d t t 2 ⁢ Q 1 ⁢ ( t ) ⁢ Q 2 ⁢ ( t ) = 1 3 ⁢ b 1 ⁢ b 2 ⁢ R D ⁡ ( U 2 + a 1 ⁢ b 2 , U 2 + a 2 ⁢ b 1 , U 2 ) + ( x ⁢ y ⁢ U ) - 1 , superscript subscript 𝑦 𝑥 𝑡 superscript 𝑡 2 subscript 𝑄 1 𝑡 subscript 𝑄 2 𝑡 1 3 subscript 𝑏 1 subscript 𝑏 2 Carlson-integral-RD superscript 𝑈 2 subscript 𝑎 1 subscript 𝑏 2 superscript 𝑈 2 subscript 𝑎 2 subscript 𝑏 1 superscript 𝑈 2 superscript 𝑥 𝑦 𝑈 1 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{t^{2}\sqrt{Q_{1}(t)% Q_{2}(t)}}=\tfrac{1}{3}b_{1}b_{2}R_{D}\left(U^{2}+a_{1}b_{2},U^{2}+a_{2}b_{1},% U^{2}\right)+(xyU)^{-1},}}
    0 references
    DLMF id
    DLMF:19.29.E21
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    test
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
     
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